hermitianeigenvector

The eigenvalues and eigenvectors of Hermitian matrices have some special properties. First of all, the eigenvalues must be real!

In mathematics, a Hermitian matrix (or self-adjoint matrix) is a complex square matrix that is equal to its own conjugate transpose—that is, the element in ...

2013年10月15日 — Let L be a linear operator on some given vector space V . A scalar λ and a nonzero vector v are referred to, respectively, as an eigenvalue and ...

2014年4月21日 — Let's write the problem in a better way. You have a Hermitian matrix A, two distinct eigenvalues λ and μ and two eigenvectors v≠0, ...

2017年9月14日 — Consider a Hermitian matrix M=M†. Clearly, its eigenvalues are real, but what is the condition for the eigenvectors to be real as well?

2016年9月21日 — In a Hermitian Matrix, the Eigenvectors of Different Eigenvalues are Orthogonal ... This is an elementary (yet important) fact in matrix analysis.

2017年2月24日 — M is Hermitian iff all its eigenvalues are real. If further M is real and symmetric, then all its eigenvectors have real entries as well.

Spectral theorem for unitary matrices. For a unitary matrix,. (i) all eigenvalues have absolute value 1,. (ii) eigenvectors corresponding to distinct ...